Take-home Exercise 2

0. Goals & Objectives.

Our goal is to conduct a case study to demonstrate the potential value of Geospatial Data Science & Analysis, by integrating publicly available data from multiple sources to build a spatial interaction models, to determine factors affecting urban mobility patterns of public bus transit.

Recentdeployments of massively pervasive computing technologies such as in-vehicle GPS and SMART cards by public transport provide plenty of data for tracking movement patterns through space and time, but the explosive growth of data has outstripped public services’ ability to utilise, transform, and understand the data.

More detail about the task from: https://isss624-ay2023-24nov.netlify.app/take-home_ex02

Modifible Areal Unit Problem (MAUP): - MPSZ is too coarse, too huge a subzone area; people may live only in a corner of the subzone - Planning subzones too large, so we use analytical hexagon

“Map is not interesting, pattern revealed by and factors affecting the map is interesting. Can we explain this by building a spatial model?” - Building a model to explain flows; Spatial Interaction Model

GLM: Generalised Linear-Regression Model (over linear model):

• Dwelling Units as proxy for population;
• Can compare HDB-only VS dwelling units vs room-flat vs 1/2/3/ room flat unit
• POI: points of interest name & type

Important Note

Due to the nature of EDA and Data Analysis, parts of this page have been Collapsed or placed behind tabs, to avoid excessive scrolling.

For easier reading, this study is also presented in point-form.

0.1 Dataset used

0.1.1 Aspatial Dataset

Dataset, Purpose & Source:	Key columns
hdb.csv : HDB Property information data with geocoding Via data.gov	lat, long: coordinates | max_floors, total_dwelling_units : idea of how many units each HDB holds
origin_destination_bus_202310 : Volume of bus passenger trips, by origin/destination, data prepared for 2023 October Via LTA DataMall	ORIGIN_PT_code, DESTINATION_PT_code: O/D information on bus trip TIME_PER_HOUR, DAY_TYPE: Time/Date data on when the trips were taken TOTAL_TRIPS: Bus trip passenger volume

0.1.2 Geospatial Dataset

Sample grid table. |

Filename, Purpose & Source:	Key columns
hdb.csv : HDB Property information data with geocoding Via data.gov	lat, long: coordinates | max_floors, total_dwelling_units : idea of how many units each HDB holds
origin_destination_bus_202310 : Volume of bus passenger trips, by origin/destination, data prepared for 2023 October Via LTA DataMall	ORIGIN_PT_code, DESTINATION_PT_code: O/D information on bus trip TIME_PER_HOUR, DAY_TYPE: Time/Date data on when the trips were taken TOTAL_TRIPS: Bus trip passenger volume

1. Geospatial Data Wrangling

This study was performed in R, written in R Studio, and published using Quarto.

1.1 Import Packages

This function calls pacman to load sf, tidyverse, tmap, knitr packages;

• tmap : For thematic mapping; powerful mapping package;
• sf : for geospatial data handling, but also geoprocessing: buffer, point-in-polygon count, etc;
• sp : for spDists() at high speed
• reshape2 : for melt() instead of pivot_longer()
• sfdep : useful functions for creating weight matrix, LISA calculations etc;
• tidyverse : for non-spatial data handling; commonly used R package and contains dplyr for dataframe manipulation and ggplot for data visualization;
• DT: for displaying datatables;
• leaflet: for custom layer controls over tmap visualisations.
• stplanar: for creating desire lines to visualize O/D flows

pacman::p_load(tmap, sf, sfdep, tidyverse, DT, leaflet, stplanr, sp, reshape2)

devtools::install_github("thomasp85/patchwork")

Skipping install of 'patchwork' from a github remote, the SHA1 (51a6eff5) has not changed since last install.
  Use `force = TRUE` to force installation

library(patchwork)

1.2 Import Geospatial Data

1.2.1 raw_bus_stop_sf: Load Geospatial Bus Stop Data

• First, we load BusStop shapefile data from LTA Datamall;
• st_read() is used to import the ESRI Shapefile data into an sf dataframe.
  • From previous take-home exercise, we know BusStop has the incorrect CRS (coordinate reference system), as EPSG 9001 instead of 3414, so we use st_set_crs() to correct this
  • We use head() to preview the first 6 rows

show code

raw_bus_stop_sf <- st_read(dsn = "data/geospatial", 
                 layer = "BusStop") %>%
  st_set_crs(3414)

Reading layer `BusStop' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 5161 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21

Warning: st_crs<- : replacing crs does not reproject data; use st_transform for
that

show code

head(raw_bus_stop_sf)

Simple feature collection with 6 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 13228.59 ymin: 30391.85 xmax: 41603.76 ymax: 44206.38
Projected CRS: SVY21 / Singapore TM
  BUS_STOP_N BUS_ROOF_N             LOC_DESC                  geometry
1      22069        B06   OPP CEVA LOGISTICS POINT (13576.31 32883.65)
2      32071        B23         AFT TRACK 13 POINT (13228.59 44206.38)
3      44331        B01              BLK 239  POINT (21045.1 40242.08)
4      96081        B05 GRACE INDEPENDENT CH POINT (41603.76 35413.11)
5      11561        B05              BLK 166 POINT (24568.74 30391.85)
6      66191        B03         AFT CORFE PL POINT (30951.58 38079.61)

• We check the coordinate reference system with st_crs(); and see that it is now indeed correctly set to 3414:

EXPAND To See: Full st_crsReadout

show code

st_crs(raw_bus_stop_sf)

Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

• We use qtm() to perform a quick visualization of the various bus stops:

show code

tmap_mode("plot")

tmap mode set to plotting

show code

qtm(raw_bus_stop_sf)

1.2.2 mpsz_sf: Visualizing Singapore’s Master Plan 2019 Subzone Boundaries

• We now load Master Plan 2019 Subzone Boundary

• Next, we load MPSZ-2019 shapefile data from Data.gov.sg, comprising Master Plan 2019 Subzone Boundary (No Sea) data ;

• st_read() is used to import the ESRI Shapefile data into an sf dataframe;

  • We use st_crs() to check the Coordinate Reference System (CRS);

show code

mpsz_sf <- st_read(dsn = "data/geospatial", 
                 layer = "MPSZ-2019") 

Reading layer `MPSZ-2019' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84

show code

st_crs(mpsz_sf)

Coordinate Reference System:
  User input: WGS 84 
  wkt:
GEOGCRS["WGS 84",
    DATUM["World Geodetic System 1984",
        ELLIPSOID["WGS 84",6378137,298.257223563,
            LENGTHUNIT["metre",1]]],
    PRIMEM["Greenwich",0,
        ANGLEUNIT["degree",0.0174532925199433]],
    CS[ellipsoidal,2],
        AXIS["latitude",north,
            ORDER[1],
            ANGLEUNIT["degree",0.0174532925199433]],
        AXIS["longitude",east,
            ORDER[2],
            ANGLEUNIT["degree",0.0174532925199433]],
    ID["EPSG",4326]]

• We see that MPSZ-2019 is set to WGS 84/EPSG 4326 projection, which is inconsistent with the rest of our dataset;
• Thus, we use st_transform() to reproject the data to SVY21/EPSG 3414 Coordinate Reference System (CRS) to ensure consistent distance calculation:

show code

mpsz_sf <- mpsz_sf %>%
  st_transform(crs=3414)
st_crs(mpsz_sf)

Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

• Now, let’s visualize the bus stop within the mpsz subzone boundaries;
• We set tmap_mode("plot") to allow us to scroll;
• We use tm_shape() + tm_polygons() to map a base layer of the mpsz boundaries;
  • On top of which, we layer tm_shape() + tm_dots() to show the bus stops.

show code

tmap_mode("plot")

tmap mode set to plotting

show code

tmap_options(check.and.fix = TRUE)
tm_shape(mpsz_sf) +
  tm_polygons() + 
  tm_shape(raw_bus_stop_sf) + 
  tm_dots()

Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

• We note there are a number of bus stops outside Singapore’s boundaries; Specifically, three bus stops in a cluster just outside the Causeway, and one further North.
• We perform several steps to isolate & check the data;
  • we use st_filter() to find bus stops within Singapore’s Administrative National Boundaries, and create sg_bus_stop_sf for future use.
  • to check what bus stops have been dropped, we use anti_join() to compare raw_bus_stop_sf with sg_bus_stop_sf. We use st_drop_geometry on both sf dataframes to only compare the non-geometry columns.

show code

sg_bus_stop_sf <- st_filter(raw_bus_stop_sf, mpsz_sf)
anti_join(st_drop_geometry(raw_bus_stop_sf), st_drop_geometry(sg_bus_stop_sf))

Joining with `by = join_by(BUS_STOP_N, BUS_ROOF_N, LOC_DESC)`

  BUS_STOP_N BUS_ROOF_N            LOC_DESC
1      47701        NIL          JB SENTRAL
2      46239         NA          LARKIN TER
3      46609         NA     KOTARAYA II TER
4      46211        NIL JOHOR BAHRU CHECKPT
5      46219        NIL JOHOR BAHRU CHECKPT

• We see there are in fact 5 bus stops outside of Singapore (including the defunct Kotaraya II Terminal) that have been removed, which means our data cleaning was correct.

1.3 Geospatial Data Cleaning

1.3.1 Removing Duplicate Bus Stops

• From Take-home Exercise 1, we know that there are a number of repeated bus stops. We repeat some steps;
• We use length() to find the total number of raw values in the $BUS_STOP_N column of sg_bus_stop_sf;
  • We then compare this to length(unique()) to find the unique values;
• And, indeed, we find there are 16 bus stops that are repeated;

cat("\nResults before removing duplicates: \n=======================================================\n")

Results before removing duplicates: 
=======================================================

cat("Total number of rows in sg_bus_stop_sf\t\t: ", paste0(length(sg_bus_stop_sf$BUS_STOP_N)))

Total number of rows in sg_bus_stop_sf      :  5156

cat("\nTotal unique bus stop IDs in sg_bus_stop_sf\t: ", paste0(length(unique(sg_bus_stop_sf$BUS_STOP_N))))

Total unique bus stop IDs in sg_bus_stop_sf :  5140

cat("\nRepeated bus stops\t\t\t\t:   ", paste0(length(sg_bus_stop_sf$BUS_STOP_N) - length(unique(sg_bus_stop_sf$BUS_STOP_N))))

Repeated bus stops              :    16

• It appears there are 16 datapoints that are specifically repeated; let’s remove them by deleting the duplicated rows:
  • we use duplicated() to identify rows with repeated values of $BUS_STOP_N; duplicated rows will return TRUE while all other rows will return FALSE
  • We use ! to invert the values, so only the unduplicated rows will return TRUE.
  • We then use square brackets [] to index sg_bus_stop_sf based on the rows, and return only the unduplicated rows;
  • We then assign the output using <- into bus_stop_sf, for use.

show code

bus_stop_sf <- sg_bus_stop_sf[!duplicated(sg_bus_stop_sf$BUS_STOP_N), ]
head(bus_stop_sf)

Simple feature collection with 6 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 13228.59 ymin: 30391.85 xmax: 41603.76 ymax: 44206.38
Projected CRS: SVY21 / Singapore TM
  BUS_STOP_N BUS_ROOF_N             LOC_DESC                  geometry
1      22069        B06   OPP CEVA LOGISTICS POINT (13576.31 32883.65)
2      32071        B23         AFT TRACK 13 POINT (13228.59 44206.38)
3      44331        B01              BLK 239  POINT (21045.1 40242.08)
4      96081        B05 GRACE INDEPENDENT CH POINT (41603.76 35413.11)
5      11561        B05              BLK 166 POINT (24568.74 30391.85)
6      66191        B03         AFT CORFE PL POINT (30951.58 38079.61)

show code

cat("\nResults after removing duplicates: \n=======================================================\n")

Results after removing duplicates: 
=======================================================

show code

cat("Total number of rows in bus_stop_sf\t\t: ", paste0(length(bus_stop_sf$BUS_STOP_N)))

Total number of rows in bus_stop_sf     :  5140

show code

cat("\nTotal unique bus stop IDs in bus_stop_sf\t: ", paste0(length(unique(bus_stop_sf$BUS_STOP_N))))

Total unique bus stop IDs in bus_stop_sf    :  5140

show code

cat("\nRepeated bus stops\t\t\t\t:   ", paste0(length(bus_stop_sf$BUS_STOP_N) - length(unique(bus_stop_sf$BUS_STOP_N))))

Repeated bus stops              :    0

• We can do a quick check to visualize these;
  • We use tmap_mode("view") to allow us to scroll around and check that the bus stops fall within Singapore’s national boundaries, and set zoom limits to focus the attention
  • We combine tm_shape() and tm_polygons() to map the master plan subzones in grey;
  • We combine tm_shape() and tm_dots() to map locations of bus stops; for visual distinction with the grey zones, we use the “Spectral” palette

show code

tmap_mode("view")

tmap mode set to interactive viewing

show code

tm_shape(mpsz_sf) +
  tm_polygons() + 
  tm_shape(bus_stop_sf) + 
  tm_dots(col = "BUS_STOP_N", palette = "Spectral", legend.show = FALSE) + 
  tm_view(set.zoom.limits = c(11, 13))

Warning: The shape mpsz_sf is invalid (after reprojection). See sf::st_is_valid

Warning: Number of levels of the variable "BUS_STOP_N" is 5140, which is larger
than max.categories (which is 30), so levels are combined. Set
tmap_options(max.categories = 5140) in the layer function to show all levels.

show code

tmap_mode("plot")

tmap mode set to plotting

• Now, we can start preparing the hexagon map.

1.4 Generating Hexagon Maps

• We generate the hexagon map in three steps:

1. We use st_make_grid() with square = FALSE to create the hexagon layer as defined in the study, which we name raw_hex_grid;
   • We pass cellsize = 750 to create the hexagons of necessary size. Prof Kam defined the apothem as 375m, as the Traffic Analysis Zone is typically 750m in size.
   • I used units::as_units to pass 750 metres into the argument. I am still uncertain whether a length of 750m needs to be reprojected, or whether we need to do any further transformation.
   • We use st_transform() just in case we need to reproject the coordinate system, just in case.
2. We use st_sf() to convert raw_hex_grid into an sf dataframe for further manipulation later; - However, trying to visualize this right now just gives us a map full of hexagons, so need to eliminate the empty hexagons; - We use mutate() to create a new column, $n_bus_stops that counts the number of bus stops in each hexagon using lengths(st_intersects())
   • st_intersects() gives us a list of bus stops in each hexagon, so we use lengths() to count the number
3. We create our final sf dataframe, hexagon_sf in two steps; - First, we use filter() to select only hexagons with nonzero number of bus stops; - Then, mutate() is used here to create a grid_id column, labelling only the hexagons with nonzero bus stops.

• Finally, we perform a quick plot to confirm that every bus stop is inside a hexagon;
  • Using hexagon_sf as our base layer, we use tmap_shape() and tm_polygons() to visualizes our hexes. We pass palette = "Spectral" for visual distinguishment against the black dots of the bus stops.
  • We use tmap_shape() and tm_dots() to visualize our bus stop as black dots

show code

# STEP 1 - Create hexagon map 
raw_hex_grid <- st_make_grid(bus_stop_sf, cellsize = units::as_units(375, "m"), what = "polygons", square = FALSE) %>%
  st_transform(crs = 3414)

# STEP 2 - Convert to sf object and count the number of bus stops inside;
raw_hex_grid <- st_sf(raw_hex_grid) %>%
  mutate(n_bus_stops = lengths(st_intersects(raw_hex_grid, sg_bus_stop_sf))) 

# Count number of points in each grid, code snippet referenced from: 
# https://gis.stackexchange.com/questions/323698/counting-points-in-polygons-with-sf-package-of-r


# STEP 3 - Filter for nonempty hexes and label:

hexagon_sf <- filter(raw_hex_grid, n_bus_stops > 0) 
hexagon_sf <- hexagon_sf %>%
  mutate(grid_id = 1:nrow(hexagon_sf)) %>%
  select(grid_id, raw_hex_grid, n_bus_stops)

tmap_mode("plot")

tmap mode set to plotting

show code

tm_shape(hexagon_sf) +
  tm_polygons(col = "grid_id", palette = "Spectral", legend.show = FALSE) + 
  tm_shape(bus_stop_sf) + 
  tm_dots()

show code

tmap_mode("plot")

tmap mode set to plotting

• We can visually confirm that every black dot is within a hexagon.
• We re-use a bit of code from Take-Home Exercise 1 to plot our analytical hexagons on a map of Singapore and visualize the number of bus stops in each hexagon:

show code

tmap_mode("view")

tmap mode set to interactive viewing

show code

tm_basemap(providers$OneMapSG.Grey) + 
  tm_shape(hexagon_sf) +
  tm_fill(
    col = "n_bus_stops",
    palette = "-plasma",
    style = "cont",
    
    breaks = c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12),
    title = "Number of bus_stops",
    id = "grid_id",
    showNA = FALSE,
    alpha = 0.6,
    popup.vars = c(
      "Number of Bus Stops: " = "n_bus_stops"
    ),
    popup.format = list(
      n_bus_stops = list(format = "f", digits = 0)
    )
  ) +
  tm_borders(col = "grey40", lwd = 0.7)  + 
  tm_view(set.zoom.limits = c(11, 13))

show code

tmap_mode("plot")

tmap mode set to plotting

• We perform some simple stats to count the total number of filtered hexagons, and to see the maximum number of bus stops in a hexagon.
  • Unlike Take-Home Exercise 1, the number of hexagons have decreased, and the maximum number of bus stops per hexagon is lower.

show code

# NB: Code reused from my own take-home exercise 1
cat(paste("Total number of raw hexagons is\t\t\t: ", nrow(raw_hex_grid), "\n"))

Total number of raw hexagons is         :  8843 

show code

cat(paste("Total number of hexagons (n_bus_stop > 1) is\t: ", nrow(hexagon_sf)), "\n")

Total number of hexagons (n_bus_stop > 1) is    :  2172 

show code

cat("\nPrinting map_hexagon_sf:\n >> ")

Printing map_hexagon_sf:
 >> 

show code

hexagon_sf[hexagon_sf$n_bus_stops > 5, ]

Simple feature collection with 47 features and 2 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 10532.62 ymin: 29837.95 xmax: 42782.62 ymax: 47807.98
Projected CRS: SVY21 / Singapore TM
First 10 features:
    grid_id n_bus_stops                   raw_hex_grid
149     149           6 POLYGON ((10720.12 34059.82...
170     170           6 POLYGON ((11470.12 34059.82...
191     191           6 POLYGON ((12032.62 35683.62...
214     214           6 POLYGON ((12595.12 36008.38...
217     217           6 POLYGON ((12595.12 39255.98...
297     297           6 POLYGON ((14282.62 35034.1,...
347     347           7 POLYGON ((15782.62 34384.58...
405     405           6 POLYGON ((17470.12 39905.49...
426     426           6 POLYGON ((17845.12 39905.49...
441     441           6 POLYGON ((18032.62 40230.25...

• For the next step, we’ll need to manage the aspatial bus trips dataset, which is what we’ll work on now.

1.5 Aspatial Data Wrangling: Bus trip dataset

1.5.1 Import Bus O/D Dataset

• For our purposes, we will focus only on 2023-October Passenger Volume by Origin Destination Bus Stops, downloaded from LTA DataMall;

• We use read_csv() to load the data from the .csv file;

• We use select() with a - sign to remove two columns redundant for our analysis:

  • $PT_TYPE column indicates the type of public transport, however, every value is “BUS”
  • $YEAR_MONTH column similarly has “2023-10” for every value, which we are aware of
  • With this in mind, we drop these two columns to save space.

• Finally, we use mutate_at() to convert two columns ($ORIGIN_PT_CODE and $DESTINATION_PT_CODE)from character to factor, for easier analysis.

• We use str() to check the columns, datatypes, and number of rows:

show code

odbus_2310 <- read_csv("data/aspatial/origin_destination_bus_202310.csv") %>%
  select( -PT_TYPE, -YEAR_MONTH) %>%
  mutate_at(c("ORIGIN_PT_CODE", "DESTINATION_PT_CODE"), as.factor)

Rows: 5694297 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (5): YEAR_MONTH, DAY_TYPE, PT_TYPE, ORIGIN_PT_CODE, DESTINATION_PT_CODE
dbl (2): TIME_PER_HOUR, TOTAL_TRIPS

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

show code

str(odbus_2310)

tibble [5,694,297 × 5] (S3: tbl_df/tbl/data.frame)
 $ DAY_TYPE           : chr [1:5694297] "WEEKENDS/HOLIDAY" "WEEKDAY" "WEEKENDS/HOLIDAY" "WEEKDAY" ...
 $ TIME_PER_HOUR      : num [1:5694297] 16 16 14 14 17 17 17 7 14 14 ...
 $ ORIGIN_PT_CODE     : Factor w/ 5073 levels "01012","01013",..: 105 105 4428 4428 2011 834 834 781 4462 4462 ...
 $ DESTINATION_PT_CODE: Factor w/ 5077 levels "01012","01013",..: 240 240 4742 4742 693 809 809 235 4002 4002 ...
 $ TOTAL_TRIPS        : num [1:5694297] 3 5 3 5 4 1 24 2 1 7 ...

• This is a huge tibble dataframe with over 5 million rows, so we will filter this now by peaks;
• For this study, we focus on Weekday afternoon peak

1.5.2 Filter For Peaks – Weekday Afternoon

• We now perform a multi-step filter process;
  1. We combine mutate() with case_when() to create a new column, $PEAK, based on the study criteria:
     1. We set the value to “WEEKDAY_AFTERNOON_PEAK” if $DAY_TYPE is “WEEKDAY” and bus tap-on time (e.g. $TIME_PER_HOUR) is between 5 pm and 8pm, inclusive;
        • Note that we convert the values for $TIME_PER_HOUR to 24-hour clock, e.g. “5pm” is “17” hundred hours, “8pm” is “20” hundred hours.
     2. For all remaining values, we assign an “Unknown” value.
  2. We then use filter() to eliminate those with “Unknown” $PEAK values, i.e. rows outside the period of interest for the study
  3. We use group_by() to group the values by $ORIGIN_PT_CODE and $DESTINATION_PT_CODE, and use summarise() to aggregate the sum of $TOTAL_TRIPS as a new column, $TRIPS.
  4. We use write_rds() to save the output dataframe, odbus_filtered, as an RDS object for future reference/load.

odbus_filtered <- odbus_2310 %>%
  mutate(PEAK = case_when(
    DAY_TYPE == "WEEKDAY" & TIME_PER_HOUR >= 17 &  TIME_PER_HOUR <= 20 ~ "WEEKDAY_AFTERNOON_PEAK",
    TRUE ~ "Unknown"
  )) %>%
  filter(
    case_when(
      PEAK == "Unknown" ~ FALSE,
      TRUE ~ TRUE
    )) %>%
  group_by(ORIGIN_PT_CODE, DESTINATION_PT_CODE) %>%
  summarise(TRIPS = sum(TOTAL_TRIPS))

`summarise()` has grouped output by 'ORIGIN_PT_CODE'. You can override using
the `.groups` argument.

write_rds(odbus_filtered, "data/rds/odbus_filtered_weekday.rds")
head(odbus_filtered)

# A tibble: 6 × 3
# Groups:   ORIGIN_PT_CODE [1]
  ORIGIN_PT_CODE DESTINATION_PT_CODE TRIPS
  <fct>          <fct>               <dbl>
1 01012          01112                 540
2 01012          01113                 516
3 01012          01121                 303
4 01012          01211                 363
5 01012          01311                 630
6 01012          01549                   6

1.6 Combine Bus Trip Data With hexagon_sf Dataframe

• For our study purposes, we need to have the number of bus trips originating from each hexagon. In order to achieve this, we must combine our three current dataframes:
  • hexagon_sf, an sf dataframe with $grid_id column (primary key) and the specific polygon geometry of each hexagon;
  • bus_stop_sf, an sf dataframe with the $BUS_STOP_N (primary key) and the point geometry of each bus stop;
  • odbus_filtered, a tibble dataframe with the $ORIGIN_PT_CODE (primary key) column and the trip details for each of the four peak periods of interest.

1.6.1 bus_stop_hexgrid_id: Identify Hexagon grid_id For Each Bus Stop

• First, we combine hexagon_sf with sg_bus_stop_sf ;
  • We use st_intersection to combine the dataframes such that each row of sg_bus_stop_sf has an associated grid_id;
  • We use select() to filter the resultant bus_stop_hexgrid_id dataframe to only $grid_id and $BUS_STOP_N columns, and use st_drop_geometry() to convert into a simple dataframe with just two columns:

show code

bus_stop_hexgrid_id <- st_intersection(bus_stop_sf, hexagon_sf) %>%
  select(BUS_STOP_N, grid_id) %>%
  st_drop_geometry()

Warning: attribute variables are assumed to be spatially constant throughout
all geometries

show code

cat("\nNumber of bus stops\t:", length(unique(bus_stop_hexgrid_id$BUS_STOP_N)))

Number of bus stops : 5140

show code

cat("\nNumber of hexgrids\t:", length(unique(bus_stop_hexgrid_id$grid_id)))

Number of hexgrids  : 2170

show code

head(bus_stop_hexgrid_id)

       BUS_STOP_N grid_id
3265        25059       1
3265.1      25059       2
2566        25751       3
254         26379       4
2399        26369       5
2893        25761       6

• Eagle-eyed readers may notice that BUS_STOP_N #25059 is in both $grid_id 1 & 2;
• Let’s check if there’s any other duplicates:

show code

bus_stop_hexgrid_id$BUS_STOP_N[duplicated(bus_stop_hexgrid_id$BUS_STOP_N)]

[1] "25059"

• Only BUS_STOP_N #25059 is duplicated; let’s see why this is:

show code

tmap_mode("view")

tmap mode set to interactive viewing

show code

tm_shape(hexagon_sf[hexagon_sf$grid_id %in% c(1, 2),]) +
  tm_polygons(col = "grid_id", palette = "Spectral") + 
  tm_shape(bus_stop_sf[bus_stop_sf$BUS_STOP_N %in% c(25059),]) + 
  tm_dots()

show code

tmap_mode("plot")

tmap mode set to plotting

• It appears that BUS_STOP_N #25059 is exactly on the boundary between the two hexagons.
• Here we perform simple manual intervention data cleaning, declaring the bus stop is in $grid_id 2 by deleting the first row;
  • We use subset() to select values of $grid_id that are not equal to 1

show code

bus_stop_hexgrid_id <- subset(bus_stop_hexgrid_id, grid_id != 1)

cat("\nNumber of bus stops\t:", length(unique(bus_stop_hexgrid_id$BUS_STOP_N)))

Number of bus stops : 5140

show code

cat("\nNumber of hexgrids\t:", length(unique(bus_stop_hexgrid_id$grid_id)))

Number of hexgrids  : 2169

show code

cat("\n\nPrinting rows with duplicated bus stop values\t:", bus_stop_hexgrid_id$BUS_STOP_N[duplicated(bus_stop_hexgrid_id$BUS_STOP_N)])

Printing rows with duplicated bus stop values   : 

show code

cat("\n\n(If empty, it worked!)")

(If empty, it worked!)

• Now we append hexagon code onto odbus_filtered. We do this in two steps;
• First, we use left_join() to add the hexagon $grid_id by BUS_STOP_N number;
  • We use rename() to rename columns, and specify the origin bus stop and origin hex grid id as ORIGIN_BS and ORIGIN_HEX respectively;
  • We create a duplicate tibble data.frame to check for duplicate results, and luckily we see an empty tibble

show code

od_data <- left_join(odbus_filtered , bus_stop_hexgrid_id,
            by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
  rename(ORIGIN_BS = ORIGIN_PT_CODE,
         ORIGIN_HEX = grid_id)
duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
duplicate

# A tibble: 0 × 4
# ℹ 4 variables: ORIGIN_BS <chr>, DESTINATION_PT_CODE <fct>, TRIPS <dbl>,
#   ORIGIN_HEX <int>

show code

# od_data[!complete.cases(od_data), ]
# 
# bus_stop_hexgrid_id[] 
# hexagon_sf[hexagon_sf$grid_id %in% c(1, 2),]

# bus_stop_hexgrid_id[bus_stop_hexgrid_id$BUS_STOP_N %in% c(03361),]

# 
# raw_bus_stop_sf[raw_bus_stop_sf$BUS_STOP_N %in% c(03361, 03549, 03579, 59009),]

• Now we repeat the step, appending the destination hex ID

show code

od_data <- left_join(od_data , bus_stop_hexgrid_id,
            by = c("DESTINATION_PT_CODE" = "BUS_STOP_N")) %>%
  rename(DESTIN_BS = DESTINATION_PT_CODE,
         DESTIN_HEX = grid_id)
duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
duplicate

# A tibble: 0 × 5
# ℹ 5 variables: ORIGIN_BS <chr>, DESTIN_BS <chr>, TRIPS <dbl>,
#   ORIGIN_HEX <int>, DESTIN_HEX <int>

show code

# od_data[!complete.cases(od_data), ]

• Once again, we have an empty tibble.
• We finally create the final version of our flow dataset.
  • Just to be safe, we perform a step to remove duplicates using unique()
  • drop_na() removes bus stops for which we have no info. It turns out there are bus stop numbers outside our bus stop dataset, like 03361, 03549, 03579, 59009;
    • Some of these may be new bus stops, like 03361, Gardens by the Bay Stn Exit 2, and 03549
  • We use group_by() to combine rows with the same $ORIGIN_HEX and $DESTIN_HEX, and aggregate the number of trips with summarise()

show code

od_data <- od_data %>%
  unique() %>%
  drop_na() %>%
  group_by(ORIGIN_HEX, DESTIN_HEX) %>%
  summarise(SUM_TRIPS = sum(TRIPS))

`summarise()` has grouped output by 'ORIGIN_HEX'. You can override using the
`.groups` argument.

show code

head(od_data)

# A tibble: 6 × 3
# Groups:   ORIGIN_HEX [1]
  ORIGIN_HEX DESTIN_HEX SUM_TRIPS
       <int>      <int>     <dbl>
1          2          6         3
2          2         13        34
3          2         20       182
4          2         37         1
5          2         50        18
6          2         53         1

• Now we write the output to RDS

show code

write_rds(od_data, "data/rds/od_data.rds")
od_data <- read_rds("data/rds/od_data.rds")

• Remove intrazonal flows

show code

od_data1 <- od_data[od_data$ORIGIN_HEX!=od_data$DESTIN_HEX,]

• Create desire lines

show code

flowLine <- od2line(flow = od_data1, 
                    zones = hexagon_sf,
                    zone_code = "grid_id")

Creating centroids representing desire line start and end points.

show code

summary(od_data1$SUM_TRIPS)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    1.0     4.0    17.0   129.6    66.0 73720.0 

• Quick exploration: most values are below 500

show code

lplot <- ggplot(data = flowLine, aes(x=SUM_TRIPS, y=ORIGIN_HEX)) +
  geom_point()  +
  labs(title = "Histogram with Different Fill Colors",
       x = "Value",
       y = "Frequency") + 
  geom_vline(xintercept = 1000, colour="red")
rplot1 <- ggplot(data = flowLine, 
                aes(x=SUM_TRIPS)) +
  geom_histogram(breaks=seq(0, 20000, by = 1000)) + 
  geom_vline(xintercept = 1000, colour="red")
rplot2 <- ggplot(data = flowLine, 
                aes(x=SUM_TRIPS)) +
  geom_histogram(breaks=seq(0, 2000, by = 500)) + 
  geom_vline(xintercept = 1000, colour="red")

lplot / (rplot1 + rplot2)

custom_palette <- c('#fee090','#d73027','#72001a', '#313695')
tmap_mode("plot")

tmap mode set to plotting

tm_shape(hexagon_sf) +
  tm_polygons() +
flowLine %>%  
  filter(SUM_TRIPS >= 1000) %>%  
  tm_shape() +
  tm_lines(col = "SUM_TRIPS",
           lwd = "SUM_TRIPS",
           palette = custom_palette,
           style = "fixed",
           breaks = c(1000, 2000, 4000, 8000, 100000),
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.8)

• Plotting trips over 10,000:
  • 150 trips over 10,000
  • 20 trips over 20,000

flowLine[flowLine$SUM_TRIPS>=20000,]

Simple feature collection with 20 features and 3 fields
Geometry type: LINESTRING
Dimension:     XY
Bounding box:  xmin: 12032.62 ymin: 32977.29 xmax: 41095.12 ymax: 47591.47
Projected CRS: SVY21 / Singapore TM
First 10 features:
      ORIGIN_HEX DESTIN_HEX SUM_TRIPS                       geometry
4625         279        191     20266 LINESTRING (13907.62 35900....
4637         279        204     23717 LINESTRING (13907.62 35900....
4665         279        237     30565 LINESTRING (13907.62 35900....
4675         279        253     21468 LINESTRING (13907.62 35900....
4676         279        254     23279 LINESTRING (13907.62 35900....
6903         325        309     26335 LINESTRING (15220.12 36224....
12752        427        405     49216 LINESTRING (17845.12 40771....
16829        485        516     21658 LINESTRING (18595.12 42070....
24552        594        653     59391 LINESTRING (20095.12 45318....
26612        615        587     22427 LINESTRING (20470.12 32977....

custom_palette <- c('#fee090','#fee090','#d73027','#d73027','#72001a', '#313695')
tmap_mode("plot")

tmap mode set to plotting

tm_shape(hexagon_sf) +
  tm_polygons() +
flowLine %>%  
  filter(SUM_TRIPS >= 10000) %>%  
  tm_shape() +
  tm_lines(col = "SUM_TRIPS",
           lwd = "SUM_TRIPS",
           palette = custom_palette,
           style = "jenks",,
           scale = c(1, 2, 4, 8, 10, 14),
           n = 6,
           alpha = 0.8)

show code

od_data1_origin <- od_data1 %>%
  group_by(ORIGIN_HEX) %>%
  summarise(SUM_ORIG_TRIPS = sum(SUM_TRIPS))



orig_hexagon_sf <- left_join(hexagon_sf, od_data1_origin, 
            by = c("grid_id" = "ORIGIN_HEX")) %>%
  select(grid_id, 
         SUM_ORIG_TRIPS, raw_hex_grid) %>%
  drop_na() 

ggplot(orig_hexagon_sf, aes(x = grid_id , y = SUM_ORIG_TRIPS)) +
  geom_boxplot(fill = "lightblue", color = "black", outlier.shape = 16, outlier.colour = "red") +
  geom_point(position = position_jitter(width = 0.2), color = "red", size = .5) +
  scale_y_log10() +
  labs(title = "Boxplot with Outliers Highlighted",
       x = "Category",
       y = "Value")

Warning: Continuous x aesthetic
ℹ did you forget `aes(group = ...)`?

• find top 10% of tirps by origin hexes origin

show code

origin_threshold <- quantile(orig_hexagon_sf$SUM_ORIG_TRIPS,  0.99) #237114
orig_trips_q90   <- quantile(orig_hexagon_sf$SUM_ORIG_TRIPS,  0.9) #237114
orig_trips_q99   <- quantile(orig_hexagon_sf$SUM_ORIG_TRIPS,  0.99) #237114
orig_trips_q999  <- quantile(orig_hexagon_sf$SUM_ORIG_TRIPS,  0.999) #237114
custom_origin_breaks <- c(0, orig_trips_q90, orig_trips_q99, orig_trips_q999, Inf)


# orig_hexagon_sf[orig_hexagon_sf$SUM_ORIG_TRIPS>500000,]


# custom_origin_breaks

# filter(orig_hexagon_sf, SUM_ORIG_TRIPS >= origin_threshold) 


tmap_mode("plot")

tmap mode set to plotting

show code

tm_shape(mpsz_sf) +
  tm_polygons() +
tm_shape(orig_hexagon_sf) +
  tm_polygons(col="SUM_ORIG_TRIPS", palette="YlGnBu", style = "fixed", breaks = custom_origin_breaks)

Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

show code

tmap_mode("plot")

tmap mode set to plotting

show code

tm_shape(mpsz_sf) +
  tm_polygons() +
tm_shape(filter(orig_hexagon_sf, SUM_ORIG_TRIPS >= 398408.9) ) +
  tm_polygons(col="SUM_ORIG_TRIPS", palette="-plasma") + 
flowLine %>%  
  filter(ORIGIN_HEX %in% c(279, 771, 2004)) %>%  
  tm_shape() +
  tm_lines(col = "SUM_TRIPS",
           lwd = "SUM_TRIPS",
           palette = custom_palette,
           style = "quantile",
           scale = c(1, 2, 4, 8, 10, 14),
           n = 6,
           alpha = 0.8)

Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

show code

# tm_basemap(providers$OneMapSG.Grey) + 
#   tm_shape(hexagon_sf) +
#   tm_fill(
#     col = "n_bus_stops",
#     palette = "-plasma",
#     style = "cont",
#     
#     breaks = c(0, 1, 2

• plot top 10 % of hexes by destination

show code

od_data1_destin <- od_data1 %>%
  group_by(DESTIN_HEX) %>%
  summarise(SUM_DEST_TRIPS = sum(SUM_TRIPS))



dest_hexagon_sf <- left_join(hexagon_sf, od_data1_destin, 
            by = c("grid_id" = "DESTIN_HEX")) %>%
  select(grid_id, 
         SUM_DEST_TRIPS, raw_hex_grid) %>%
  drop_na() 


dest_trips_q90   <- quantile(dest_hexagon_sf$SUM_DEST_TRIPS,  0.9) #237114
dest_trips_q99   <- quantile(dest_hexagon_sf$SUM_DEST_TRIPS,  0.99) #237114
dest_trips_q999  <- quantile(dest_hexagon_sf$SUM_DEST_TRIPS,  0.999) #237114
custom_destin_breaks <- c(0, dest_trips_q90, dest_trips_q99, dest_trips_q999, Inf)

tmap_mode("plot")

tmap mode set to plotting

show code

tm_shape(mpsz_sf) +
  tm_polygons() +
tm_shape(dest_hexagon_sf) +
  tm_polygons(col="SUM_DEST_TRIPS", palette="YlOrRd", style = "fixed", breaks = custom_origin_breaks)

Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

1.2 computing Distance matrix

• calculate & find top 10% of tirps by destin hexes

show code

hexagon_sf <- subset(hexagon_sf, grid_id != 1)
hexagon_sp <- as(hexagon_sf, "Spatial")
distance_matrix <- spDists(hexagon_sp, 
                longlat = FALSE)
head(distance_matrix, n=c(10, 10))

           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
 [1,]    0.0000  750.0000 2625.0000 3269.1742  649.5191 2341.8742 2087.9116
 [2,]  750.0000    0.0000 1948.5572 2598.0762  375.0000 1634.5871 1352.0817
 [3,] 2625.0000 1948.5572    0.0000  649.5191 2281.0359  375.0000  750.0000
 [4,] 3269.1742 2598.0762  649.5191    0.0000 2928.8436  992.1567 1352.0817
 [5,]  649.5191  375.0000 2281.0359 2928.8436    0.0000 1948.5572 1634.5871
 [6,] 2341.8742 1634.5871  375.0000  992.1567 1948.5572    0.0000  375.0000
 [7,] 2087.9116 1352.0817  750.0000 1352.0817 1634.5871  375.0000    0.0000
 [8,] 3968.6270 3269.1742 1352.0817  750.0000 3577.2720 1634.5871 1948.5572
 [9,] 1352.0817  649.5191 1718.4659 2341.8742  750.0000 1352.0817  992.1567
[10,] 1875.0000 1125.0000 1125.0000 1718.4659 1352.0817  750.0000  375.0000
          [,8]      [,9]     [,10]
 [1,] 3968.627 1352.0817 1875.0000
 [2,] 3269.174  649.5191 1125.0000
 [3,] 1352.082 1718.4659 1125.0000
 [4,]  750.000 2341.8742 1718.4659
 [5,] 3577.272  750.0000 1352.0817
 [6,] 1634.587 1352.0817  750.0000
 [7,] 1948.557  992.1567  375.0000
 [8,]    0.000 2928.8436 2281.0359
 [9,] 2928.844    0.0000  649.5191
[10,] 2281.036  649.5191    0.0000

• melt distance matrix into distance pair

show code

distPair <- melt(distance_matrix) %>%
  rename(dist = value
         , grid_id_from = Var1
         , grid_id_to = Var2)
head(distPair, 10)

   grid_id_from grid_id_to      dist
1             1          1    0.0000
2             2          1  750.0000
3             3          1 2625.0000
4             4          1 3269.1742
5             5          1  649.5191
6             6          1 2341.8742
7             7          1 2087.9116
8             8          1 3968.6270
9             9          1 1352.0817
10           10          1 1875.0000

• melt distance matrix into distance pair

show code

distPair %>%
  filter(dist > 0) %>%
  summary()

  grid_id_from    grid_id_to        dist      
 Min.   :   1   Min.   :   1   Min.   :  375  
 1st Qu.: 543   1st Qu.: 543   1st Qu.: 7875  
 Median :1086   Median :1086   Median :12898  
 Mean   :1086   Mean   :1086   Mean   :13607  
 3rd Qu.:1629   3rd Qu.:1629   3rd Qu.:18221  
 Max.   :2171   Max.   :2171   Max.   :44554  

• Minimum distance 375
• We will arbirtraitly insert 50m into interzonal distance

distPair$dist <- ifelse(distPair$dist == 0,
                        50, distPair$dist)
distPair %>%
  summary()

  grid_id_from    grid_id_to        dist      
 Min.   :   1   Min.   :   1   Min.   :   50  
 1st Qu.: 543   1st Qu.: 543   1st Qu.: 7875  
 Median :1086   Median :1086   Median :12898  
 Mean   :1086   Mean   :1086   Mean   :13600  
 3rd Qu.:1629   3rd Qu.:1629   3rd Qu.:18221  
 Max.   :2171   Max.   :2171   Max.   :44554  

write_rds(distPair, "data/rds/distPair.rds") 

1.3 prepare flow data

od_data

# A tibble: 186,031 × 3
# Groups:   ORIGIN_HEX [2,128]
   ORIGIN_HEX DESTIN_HEX SUM_TRIPS
        <int>      <int>     <dbl>
 1          2          6         3
 2          2         13        34
 3          2         20       182
 4          2         37         1
 5          2         50        18
 6          2         53         1
 7          2         54         6
 8          2         57       145
 9          3          8         2
10          3         13         4
# ℹ 186,021 more rows

od_data$od_no_intra <- ifelse(
  od_data$ORIGIN_HEX == od_data$DESTIN_HEX, 
  0, od_data$SUM_TRIPS)
od_data$offset <- ifelse(
  od_data$ORIGIN_HEX == od_data$DESTIN_HEX, 
  0.000001, 1)

# od_data$ORIGIN_HEX <- as.factor(od_data$ORIGIN_HEX)
# od_data$DESTIN_HEX <- as.factor(od_data$DESTIN_HEX)
# 
od_data_distpair <- od_data %>%
  left_join (distPair,
             by = c("ORIGIN_HEX" = "grid_id_from",
                    "DESTIN_HEX" = "grid_id_to"))
od_data_distpair

# A tibble: 186,031 × 6
# Groups:   ORIGIN_HEX [2,128]
   ORIGIN_HEX DESTIN_HEX SUM_TRIPS od_no_intra offset  dist
        <int>      <int>     <dbl>       <dbl>  <dbl> <dbl>
 1          2          6         3           3      1 1635.
 2          2         13        34          34      1 3616.
 3          2         20       182         182      1 1875.
 4          2         37         1           1      1 1635.
 5          2         50        18          18      1 5773.
 6          2         53         1           1      1 7658.
 7          2         54         6           6      1 2704.
 8          2         57       145         145      1 8017.
 9          3          8         2           2      1 1352.
10          3         13         4           4      1 1718.
# ℹ 186,021 more rows

• visualize dependent variable

ggplot(data = od_data_distpair,
       aes(x = SUM_TRIPS)) +
  geom_histogram()

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

• visualize dependent variable

ggplot(data = od_data_distpair,
       aes(x = log(dist),
           y = log(SUM_TRIPS))) +
  geom_point() +
  geom_smooth(method = lm)

`geom_smooth()` using formula = 'y ~ x'

Warning: Removed 22 rows containing non-finite values (`stat_smooth()`).

Warning: Removed 22 rows containing missing values (`geom_point()`).

• check no zero values

summary(od_data_distpair)

   ORIGIN_HEX     DESTIN_HEX     SUM_TRIPS        od_no_intra     
 Min.   :   2   Min.   :   2   Min.   :    1.0   Min.   :    0.0  
 1st Qu.: 847   1st Qu.: 827   1st Qu.:    4.0   1st Qu.:    4.0  
 Median :1276   Median :1272   Median :   17.0   Median :   17.0  
 Mean   :1238   Mean   :1237   Mean   :  129.6   Mean   :  129.1  
 3rd Qu.:1648   3rd Qu.:1657   3rd Qu.:   66.0   3rd Qu.:   66.0  
 Max.   :2172   Max.   :2172   Max.   :73720.0   Max.   :73720.0  
                                                                  
     offset              dist      
 Min.   :0.000001   Min.   :   50  
 1st Qu.:1.000000   1st Qu.: 2625  
 Median :1.000000   Median : 5073  
 Mean   :0.995931   Mean   : 6087  
 3rd Qu.:1.000000   3rd Qu.: 8738  
 Max.   :1.000000   Max.   :25334  
                    NA's   :22     

• unconstrained

uncSIM <- glm(formula = SUM_TRIPS ~ 
                log(dist),
              family = poisson(link = "log"),
              data = od_data_distpair,
              na.action = na.exclude)
uncSIM

Call:  glm(formula = SUM_TRIPS ~ log(dist), family = poisson(link = "log"), 
    data = od_data_distpair, na.action = na.exclude)

Coefficients:
(Intercept)    log(dist)  
     9.6149      -0.5881  

Degrees of Freedom: 186008 Total (i.e. Null);  186007 Residual
  (22 observations deleted due to missingness)
Null Deviance:      95130000 
Residual Deviance: 84160000     AIC: 85050000

1.6.2 Identify Bus Trip Details For Each Hexagon grid_id

• Here, we again use multiple steps to generate bus trip details for each hexagon grid_id;
  1. We use left_join() to add the grid_id to each row of odbus_filtered, since each row has a unique single bus stop ID (i.e. $BUS_STOP_N);
  2. We use select() to retain only the grid_id and the four peak-trips columns;
  3. We combine group_by() and summarise() to aggregate the trips for each peak by grid_id.
• Finally, we use head() to preview the grid_trips_df tibble dataframe.

show code

colnames(odbus_filtered)

[1] "ORIGIN_PT_CODE"      "DESTINATION_PT_CODE" "TRIPS"              

show code

grid_trips_df <- left_join(odbus_filtered, bus_stop_hexgrid_id, 
            by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
  select(grid_id, 
         TRIPS)  %>%
  group_by(grid_id) %>%
  summarise(
    TRIPS = sum(TRIPS)
    )

Adding missing grouping variables: `ORIGIN_PT_CODE`

show code

head(grid_trips_df)

# A tibble: 6 × 2
  grid_id TRIPS
    <int> <dbl>
1       2   390
2       3   114
3       4   291
4       5   241
5       6  1905
6       7   299

1.6.3 Combine Bus Trip Details Back Into hexagon_sf

• Finally, it’s time to recombine bus trip data back into hexagon_sf;
  • We use left_join on $grid_id to add trip data back into hexagon_sf;
  • We add a failsafe mutate() to replace any “NA” values for the columns.

show code

hexagon_sf <- left_join(hexagon_sf, grid_trips_df, 
            by = 'grid_id' ) %>%
  mutate(
    TRIPS = ifelse(is.na(TRIPS), 0, TRIPS)
    )

head(hexagon_sf)

Simple feature collection with 6 features and 3 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 27889.39 xmax: 4907.622 ymax: 31570
Projected CRS: SVY21 / Singapore TM
  grid_id n_bus_stops TRIPS                   raw_hex_grid
1       2           1   390 POLYGON ((4157.622 27889.39...
2       3           1   114 POLYGON ((4532.622 28538.91...
3       4           1   291 POLYGON ((4532.622 30487.47...
4       5           1   241 POLYGON ((4532.622 31136.99...
5       6           1  1905 POLYGON ((4720.122 28214.15...
6       7           1   299 POLYGON ((4720.122 30162.71...

1.7 Exploratory Data Analysis Of Bus Trips, Across Peak Periods, By Hexagons

• For ggplot, we need data in long format, so we can use gather() on grid_trips_df from Section 1.6.2 to pivot this;
• We then pipe this into a geom_boxplot() for an exploratory look:

show code

custom_breaks <- c(seq(0, 50000, by = 5000), 565000)

lplot <- ggplot(data = hexagon_sf, aes(x=TRIPS, y=grid_id)) +
  geom_point()  +
  labs(title = "Histogram with Different Fill Colors",
       x = "Value",
       y = "Frequency") + 
  geom_vline(xintercept = 20000, colour="red")
rplot <- ggplot(data = hexagon_sf[hexagon_sf$TRIPS <50001, ]
                , aes(x=TRIPS)) +
geom_histogram() + #breaks=seq(0, 50000, by = 5000) 
  geom_vline(xintercept = 20000, colour="red")

lplot / rplot

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

show code

# str(hexagon_sf$TRIPS)


# gather(grid_trips_df, key = "Peak", value = "Trips", -grid_id) %>%
#   ggplot( aes(x=grid_id, y='TRIPS', fill=grid_id)) +
#   geom_boxplot() + 
#   ggtitle("Boxplot: Trips over peak periods, 2023-Oct data") +
#     xlab("") + 
#     theme(
#       legend.position="none"
#       ) +
#   coord_flip()

Tip

We also observe that number of trips for Weekday Morning & Weekday Afternoon seems to be larger than Weekend Morning and Weekend Evening peak trips. This is also confirmed by the figure in the next section.

This means that we will have to consider Weekday and Weekend peaks on different scales.

• This is an exceptionally ugly plot, but it shows an important point: there is some serious right skew in our dataset;
• Clearly, there are some hexagons with exceptionally high trips compared to the rest of the hexagons But, could this be because some hexagons have up to 11 bus stops, while others have 1 or 2?
• We do a quick scatter plot based on $n_bus_stops to verify this:

show code

# hexagon_sf %>% 
#   st_drop_geometry() %>% 
#   pivot_longer(cols = starts_with("WEEK"),
#                names_to = "PEAK", values_to = "TRIPS") %>%
#   ggplot( aes(x=TRIPS, y=n_bus_stops, color=PEAK, shape=PEAK)) +
#   geom_point(size=2) +
#   ggtitle("Scatterplot: Trips over peak periods by number of bus stops per hexagon, 2023-Oct data") +
#     theme(legend.position=c(.85, .15),
#           legend.background = element_rect(fill = "transparent"),
#           legend.key.size = unit(0.5, "cm"),  
#           legend.text = element_text(size = 6),
#           legend.title = element_text(size = 8)
#     ) 

• Surprising results from our plot! If we consider those with > 100,000 trips as outliers, most of them come from hexagons with between 4-8 bus stops;
• There is some correlation between number of bus stops and high numbers of trips, but a stronger factor is peak time; Weekday Morning peak trips, followed by Weekday Afternoon peak trips, contribute to the largest outliers.

Tip

I note that these visualizations only scrape the surface of understanding the data. However, this is not the focus of our study; we do these quick visualizations only to provide better context for our study.